import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt
import numpy as np
from scipy import stats

df = pd.read_csv(r"C:\UNCC Freshman Year\education_dataset (1).csv")
df = pd.DataFrame(df)

df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 2000 entries, 0 to 1999
Data columns (total 26 columns):
 #   Column                  Non-Null Count  Dtype  
---  ------                  --------------  -----  
 0   student_id              2000 non-null   int64  
 1   age                     2000 non-null   int64  
 2   study_hours_per_week    2000 non-null   float64
 3   attendance_rate         2000 non-null   float64
 4   homework_completion     2000 non-null   float64
 5   reading_score           2000 non-null   float64
 6   math_score              2000 non-null   float64
 7   science_score           2000 non-null   float64
 8   parent_education_level  2000 non-null   object 
 9   family_income           2000 non-null   int64  
 10  student_ethnicity       2000 non-null   object 
 11  disability_status       2000 non-null   object 
 12  tutoring_support        2000 non-null   object 
 13  internet_access         2000 non-null   object 
 14  school_type             2000 non-null   object 
 15  region                  2000 non-null   object 
 16  social_media_hours      2000 non-null   float64
 17  gaming_hours            2000 non-null   float64
 18  num_siblings            2000 non-null   int64  
 19  locker_number           2000 non-null   object 
 20  bus_arrival_time        2000 non-null   int64  
 21  favorite_subject        2000 non-null   object 
 22  final_exam_score        2000 non-null   float64
 23  passed_course           2000 non-null   object 
 24  college_admission       2000 non-null   object 
 25  average_score           2000 non-null   float64
dtypes: float64(10), int64(5), object(11)
memory usage: 406.4+ KB

# First 5 rows of the dataframe
df.head()

df.describe()

df.describe(include='all')

# Number of missing values for each variable, none have missing values
df.isnull().sum()

student_id                0
age                       0
study_hours_per_week      0
attendance_rate           0
homework_completion       0
reading_score             0
math_score                0
science_score             0
parent_education_level    0
family_income             0
student_ethnicity         0
disability_status         0
tutoring_support          0
internet_access           0
school_type               0
region                    0
social_media_hours        0
gaming_hours              0
num_siblings              0
locker_number             0
bus_arrival_time          0
favorite_subject          0
final_exam_score          0
passed_course             0
college_admission         0
average_score             0
dtype: int64

df.shape

(2000, 26)

df.size

52000

# Number of different values; some of them have 2000 unique (direct identifiers) 
# or near it (potenitally could combine to be indirect identifiers).
# Also determines how many groups needed for categorical variables. 
df.nunique()

student_id                2000
age                          5
study_hours_per_week       166
attendance_rate            394
homework_completion        492
reading_score              465
math_score                 495
science_score              486
parent_education_level       4
family_income             1957
student_ethnicity            5
disability_status            3
tutoring_support             3
internet_access              2
school_type                  3
region                       3
social_media_hours          91
gaming_hours                72
num_siblings                 4
locker_number              801
bus_arrival_time             3
favorite_subject             5
final_exam_score           344
passed_course                2
college_admission            2
average_score              720
dtype: int64

dfnumerical = df[["age", "study_hours_per_week", "attendance_rate", "homework_completion", "reading_score", "math_score", "science_score", "family_income", "social_media_hours", "gaming_hours", "num_siblings", "final_exam_score"]]
dfnumerical

# Higher correlation between test scores and final exam scores than other variables.
sns.heatmap(dfnumerical.corr(), annot=True, cmap='coolwarm')
plt.show()

df.boxplot(column = "study_hours_per_week")

<Axes: >

df.boxplot(column = "reading_score")

<Axes: >

df.boxplot(column = "math_score")

<Axes: >

df.boxplot(column = "science_score")

<Axes: >

df.boxplot(column = "family_income")

<Axes: >

df.boxplot(column = "social_media_hours")

<Axes: >

df.boxplot(column = "gaming_hours")

<Axes: >

df.boxplot(column = "num_siblings")

<Axes: >

df.boxplot(column = "age")

<Axes: >

df.boxplot(column = "final_exam_score")

<Axes: >

df.plot.scatter(x="study_hours_per_week", y="final_exam_score")

<Axes: xlabel='study_hours_per_week', ylabel='final_exam_score'>

df.plot.scatter(x="attendance_rate", y="final_exam_score")

<Axes: xlabel='attendance_rate', ylabel='final_exam_score'>

df.plot.scatter(x="homework_completion", y="final_exam_score")

<Axes: xlabel='homework_completion', ylabel='final_exam_score'>

df.plot.scatter(x="family_income", y="final_exam_score")

<Axes: xlabel='family_income', ylabel='final_exam_score'>

df.plot.scatter(x="social_media_hours", y="final_exam_score")

<Axes: xlabel='social_media_hours', ylabel='final_exam_score'>

df.plot.scatter(x="gaming_hours", y="math_score")

<Axes: xlabel='gaming_hours', ylabel='math_score'>

df.plot.scatter(x="social_media_hours", y="gaming_hours")

<Axes: xlabel='social_media_hours', ylabel='gaming_hours'>

df.plot.scatter(x="math_score", y="reading_score")

<Axes: xlabel='math_score', ylabel='reading_score'>

df.plot.scatter(x="math_score", y="science_score")

<Axes: xlabel='math_score', ylabel='science_score'>

df.plot.scatter(x="reading_score", y="science_score")

<Axes: xlabel='reading_score', ylabel='science_score'>

# Of the variables, the most identifiable trend is one between reading_score, science_score, math_score 
# and final_exam_score which seem to have a somewhat positive trend.
sns.pairplot(dfnumerical)

<seaborn.axisgrid.PairGrid at 0x1d78e7f9f30>

dfcategorical = df[["student_id", "disability_status", "student_ethnicity", "tutoring_support", "school_type", "region", "parent_education_level", "internet_access", "college_admission", "passed_course","favorite_subject", "locker_number"]]
categoricals = df.select_dtypes(include="object").columns

# Internet access and college admission have highly imbalanced frequencies, which may create problematic minorities.

for col in categoricals:
    sns.countplot(data=df, x=col)
    plt.title(f"Barchart of {col}")
    plt.xlabel(col)
    plt.ylabel("Count")
    plt.tight_layout()
    plt.show()

df.plot.scatter(x="tutoring_support", y="final_exam_score")

<Axes: xlabel='tutoring_support', ylabel='final_exam_score'>

df.plot.scatter(x="internet_access", y="final_exam_score")

<Axes: xlabel='internet_access', ylabel='final_exam_score'>

df.plot.scatter(x="school_type", y="final_exam_score")

<Axes: xlabel='school_type', ylabel='final_exam_score'>

df.plot.scatter(x="region", y="final_exam_score")

<Axes: xlabel='region', ylabel='final_exam_score'>

df.plot.scatter(x="parent_education_level", y="final_exam_score")

<Axes: xlabel='parent_education_level', ylabel='final_exam_score'>

df.plot.scatter(x="college_admission", y="final_exam_score")

<Axes: xlabel='college_admission', ylabel='final_exam_score'>

df.plot.scatter(x="favorite_subject", y="final_exam_score")

<Axes: xlabel='favorite_subject', ylabel='final_exam_score'>

dfnumerical = df[["age", "study_hours_per_week", "attendance_rate", "homework_completion", "reading_score", "math_score", "science_score", "family_income", "social_media_hours", "gaming_hours", "num_siblings", "final_exam_score"]]
dfnumerical

dfcategorical = df[["student_id", "disability_status", "student_ethnicity", "tutoring_support", "school_type", "region", "parent_education_level", "internet_access", "college_admission", "passed_course","favorite_subject", "locker_number"]]
categoricals = df.select_dtypes(include="object").columns

group_ats = df[df['tutoring_support'] == "none"]["final_exam_score"]
group_bts = df[df['tutoring_support'] == "private"]["final_exam_score"]
group_cts = df[df['tutoring_support'] == "school"]["final_exam_score"]

f_stat, p_value = stats.f_oneway(group_ats, group_bts, group_cts)

print(f"F-statistic: {f_stat}")
print(f"P-value: {p_value}")

F-statistic: 1.0391301792138739
P-value: 0.3539534586488434

group_aia = df[df['internet_access'] == "yes"]["final_exam_score"]
group_bia = df[df['internet_access'] == "no"]["final_exam_score"]

f_stat2, p_value2 = stats.f_oneway(group_aia, group_bia)

print(f"F-statistic: {f_stat2}")
print(f"P-value: {p_value2}")

F-statistic: 0.15621909184828248
P-value: 0.6927038283601827

variable1 = df['study_hours_per_week']
variable2= df['final_exam_score']

correlation_matrix = np.corrcoef(variable1, variable2)

correlation_coefficient = correlation_matrix[0,1]

print(f"The Pearson correlation coefficient is: {correlation_coefficient}")

The Pearson correlation coefficient is: 0.04388597139243337

variable1 = df['attendance_rate']
variable2= df['final_exam_score']

correlation_matrix = np.corrcoef(variable1, variable2)

correlation_coefficient = correlation_matrix[0,1]

print(f"The Pearson correlation coefficient is: {correlation_coefficient}")

The Pearson correlation coefficient is: -0.029180875516787795

variable1 = df['homework_completion']
variable2= df['final_exam_score']

correlation_matrix = np.corrcoef(variable1, variable2)

correlation_coefficient = correlation_matrix[0,1]

print(f"The Pearson correlation coefficient is: {correlation_coefficient}")

The Pearson correlation coefficient is: -0.007697737671186041

variable1 = df['reading_score']
variable2= df['final_exam_score']

correlation_matrix = np.corrcoef(variable1, variable2)

correlation_coefficient = correlation_matrix[0,1]

print(f"The Pearson correlation coefficient is: {correlation_coefficient}")

The Pearson correlation coefficient is: 0.43939412790683136

variable1 = df['math_score']
variable2= df['final_exam_score']

correlation_matrix = np.corrcoef(variable1, variable2)

correlation_coefficient = correlation_matrix[0,1]

print(f"The Pearson correlation coefficient is: {correlation_coefficient}")

The Pearson correlation coefficient is: 0.4674740308729188

variable1 = df['science_score']
variable2= df['final_exam_score']

correlation_matrix = np.corrcoef(variable1, variable2)

correlation_coefficient = correlation_matrix[0,1]

print(f"The Pearson correlation coefficient is: {correlation_coefficient}")

The Pearson correlation coefficient is: 0.32962909455106154

variable1 = df['average_score']
variable2= df['final_exam_score']

correlation_matrix = np.corrcoef(variable1, variable2)

correlation_coefficient = correlation_matrix[0,1]

print(f"The Pearson correlation coefficient is: {correlation_coefficient}")

The Pearson correlation coefficient is: 0.7165008031621214

variable1 = df['social_media_hours']
variable2= df['final_exam_score']

correlation_matrix = np.corrcoef(variable1, variable2)

correlation_coefficient = correlation_matrix[0,1]

print(f"The Pearson correlation coefficient is: {correlation_coefficient}")

The Pearson correlation coefficient is: -0.010790465578582485

variable1 = df['gaming_hours']
variable2= df['final_exam_score']

correlation_matrix = np.corrcoef(variable1, variable2)

correlation_coefficient = correlation_matrix[0,1]

print(f"The Pearson correlation coefficient is: {correlation_coefficient}")

The Pearson correlation coefficient is: -0.03487168383776866

variable1 = df['num_siblings']
variable2= df['final_exam_score']

correlation_matrix = np.corrcoef(variable1, variable2)

correlation_coefficient = correlation_matrix[0,1]

print(f"The Pearson correlation coefficient is: {correlation_coefficient}")

The Pearson correlation coefficient is: -0.031964277957644775

variable1 = df['family_income']
variable2= df['final_exam_score']

correlation_matrix = np.corrcoef(variable1, variable2)

correlation_coefficient = correlation_matrix[0,1]

print(f"The Pearson correlation coefficient is: {correlation_coefficient}")

The Pearson correlation coefficient is: -0.012188220444990253

group_ra = df[df['region'] == "urban"]["final_exam_score"]
group_rb = df[df['region'] == "suburban"]["final_exam_score"]
group_rc = df[df['region'] == "rural"]["final_exam_score"]

f_stat2, p_value2 = stats.f_oneway(group_ra, group_rb, group_rc)

print(f"F-statistic: {f_stat2}")
print(f"P-value: {p_value2}")

F-statistic: 1.316765240207636
P-value: 0.2682334045302832

group_sta = df[df['school_type'] == "private"]["final_exam_score"]
group_stb = df[df['school_type'] == "public"]["final_exam_score"]
group_stc = df[df['school_type'] == "charter"]["final_exam_score"]

f_stat2, p_value2 = stats.f_oneway(group_sta, group_stb, group_stc)

print(f"F-statistic: {f_stat2}")
print(f"P-value: {p_value2}")

F-statistic: 0.3791471622121001
P-value: 0.684494139394759

rn = df[["reading_score", "science_score", "math_score", "study_hours_per_week"]]
rc = df[["tutoring_support", "region"]]
rn1 = df[["average_score", "study_hours_per_week"]]
rn2 = df[["reading_score", "math_score"]]
rn3 = df[["reading_score", "science_score"]]
rn4 = df[["science_score", "math_score"]]
rn5 = df[["reading_score", "study_hours_per_week"]]
rn6 = df[["science_score", "study_hours_per_week"]]
rn7 = df[["math_score", "study_hours_per_week"]]

sns.heatmap(rn.corr(), annot=True, cmap='coolwarm')
plt.show()

# Combining reading_score, science_score, and math_score because of high VIF.

from statsmodels.stats.outliers_influence import variance_inflation_factor
from statsmodels.tools.tools import add_constant

vif_data = pd.DataFrame()
vif_data["feature"] = rn.columns
vif_data["VIF"] = [variance_inflation_factor(rn.values, i) for i in range(rn.shape[1])]

print(vif_data)

                feature        VIF
0         reading_score  30.175144
1         science_score  29.539610
2            math_score  26.918671
3  study_hours_per_week  11.383586

# Removing study_hours_per_week to reduce multicollinearity.

vif_data = pd.DataFrame()
vif_data["feature"] = rn1.columns
vif_data["VIF"] = [variance_inflation_factor(rn1.values, i) for i in range(rn1.shape[1])]

print(vif_data)

                feature        VIF
0         average_score  11.379271
1  study_hours_per_week  11.379271

from scipy.stats import chi2_contingency

contingency_table = pd.crosstab(df["tutoring_support"], df["region"])

chi2, p_value, dof, expected = chi2_contingency(contingency_table)

print(f"Chi-square statistic: {chi2}")
print(f"P-value: {p_value}")
print(f"Degrees of freedom: {dof}")
print(f"Expected frequencies:\n{expected}")

Chi-square statistic: 2.837654398960902
P-value: 0.5853505355723624
Degrees of freedom: 4
Expected frequencies:
[[228.942  244.2285 237.8295]
 [212.52   226.71   220.77  ]
 [202.538  216.0615 210.4005]]

df["final_score"] = df[["reading_score", "math_score", "science_score"]].mean(axis=1)
df.head()

numeric_cols_all = df.select_dtypes(include=np.number).columns.tolist()

# We only want these numeric columns:
numeric_keep = ["math_score", "reading_score", "science_score"]

# Build df2 with EXACT columns requested
df2 = df[["final_score", "tutoring_support", "region"] + numeric_keep]

# Remove duplicates if any
df2 = df2.loc[:, ~df2.columns.duplicated()]

# Define categorical and numeric columns
categorical_cols = ["tutoring_support", "region"]
numeric_cols = ["math_score", "reading_score", "science_score"]

df2.head()

from sklearn.preprocessing import StandardScaler, OneHotEncoder
from sklearn.compose import ColumnTransformer

numeric_keep = ["math_score", "reading_score", "science_score"]

df2 = df[["final_score", "tutoring_support", "region"] + numeric_keep]

# Remove duplicated columns if any
df2 = df2.loc[:, ~df2.columns.duplicated()]

# Define categorical and numeric columns
categorical_cols = ["tutoring_support", "region"]
numeric_cols = ["math_score", "reading_score", "science_score"]

preprocessor = ColumnTransformer(
    transformers=[
        ("num", StandardScaler(), numeric_cols),
        ("cat", OneHotEncoder(drop='first'), categorical_cols)
    ]
)

# Fit and transform X (all predictors)
X = df2.drop(columns=["final_score"])
y = df2["final_score"]

X_processed = preprocessor.fit_transform(X)

# Get names of encoded categorical variables
encoded_cat_names = preprocessor.named_transformers_["cat"].get_feature_names_out(categorical_cols)

# Construct final feature names
final_feature_names = numeric_cols + list(encoded_cat_names)

# Build DataFrame
df2_processed = pd.DataFrame(X_processed, columns=final_feature_names)


df2_processed["final_score"] = y.values
df2_processed["average_score"] = df2_processed[["math_score", "reading_score", "science_score"]].mean(axis=1)
df2_processed.head()

df_model = df2_processed[
    [
        "final_score",
        "average_score",
        "tutoring_support_private",
        "tutoring_support_school",
        "region_suburban",
        "region_urban",
    ]
].copy()

df_model

df_model_y = df_model["final_score"]
df_model_X = df_model.drop(columns=["final_score"])

# We averaged performance metrics and coefficients across the folds to see how the model would perform on new data.

from sklearn.metrics import r2_score
import statsmodels.formula.api as smf
import matplotlib.pyplot as plt
import statsmodels.api as sm
from sklearn.model_selection import KFold

n_splits = 5
kf = KFold(n_splits=n_splits, shuffle=True, random_state=42)

r_squared_scores = []
rmse_scores = []
GME_urban = []
GME_suburban = []
GME_rural = []
meanprediction_urban = []
meanprediction_suburban = []
meanprediction_rural = []
intercept = []
coefficient1 = []
coefficient2 = []
coefficient3 = []
coefficient4 = []
coefficient5 = []
coefficient6 = []

fold = 1
for train_index, test_index in kf.split(df_model):
    train_data = df_model.iloc[train_index]
    xtest_data, ytest_data = df_model_X.iloc[test_index], df_model_y.iloc[test_index]

    # Fit the OLS model on the training data

    model = smf.ols(formula= """
    final_score ~ average_score
             + tutoring_support_private
             + tutoring_support_school
             + region_suburban
             + region_urban
    """, data=train_data).fit()
   
    predictions = model.predict(xtest_data)
    residuals = ytest_data - predictions
    coefficients = model.params

    intercept.append(coefficients[0])
    coefficient1.append(coefficients[1])
    coefficient2.append(coefficients[2])
    coefficient3.append(coefficients[3])
    coefficient4.append(coefficients[4])
    coefficient5.append(coefficients[5])
   
    r_squared = model.rsquared
    rmse = np.sqrt(np.mean((ytest_data - predictions)**2))

    r_squared_scores.append(r_squared)
    rmse_scores.append(rmse)


    #mean_residual_by_group = residuals2.groupby('Region')['residuals'].mean()
    #GME_urban.append(mean_residual_by_group.get('urban', 0))
    #GME_suburban.append(mean_residual_by_group.get('suburban', 0))
    #GME_rural.append(mean_residual_by_group.get('rural', 0))

    #mean_predictions_by_group = predictions2.groupby('Region')['predictions'].mean()
    #meanprediction_urban.append(mean_predictions_by_group.get('urban', 0))
    #meanprediction_suburban.append(mean_predictions_by_group.get('suburban', 0))
    #meanprediction_rural.append(mean_predictions_by_group.get('rural', 0))

    reset_test = sm.stats.linear_reset(model, use_f=True)
    print(f"\nRamsey RESET test {fold} (F-test): {reset_test}")

    plt.figure(figsize=(6, 4))
    plt.scatter(model.fittedvalues, model.resid, alpha=0.6)
    plt.axhline(0, color="red", linestyle="--")
    plt.xlabel("Fitted Values")
    plt.ylabel("Residuals")
    plt.title("Residuals vs Fitted Values")
    plt.tight_layout()
    plt.show()


    influence = model.get_influence()
    cooks_d = influence.cooks_distance
    plt.figure(figsize=(10, 6))
    plt.stem(cooks_d[0], markerfmt=",")
    plt.title("Cook's Distance Plot")
    plt.xlabel("Observation Index")
    plt.ylabel("Cook's Distance")
    plt.show()

    # print(model.summary())
    fold += 1

print(f"Mean R-squared across folds: {np.mean(r_squared_scores):.4f}")
print(f"Mean MSE across folds: {np.mean(rmse_scores):.4f}")
#print("Average Coefficient for tutoring_support_none:", round(np.mean(coefficient1), 4))
print("Average Intercept:", round(np.mean(intercept), 4))
print("Average Coefficient for average_score:", round(np.mean(coefficient1), 4))
print("Average Coefficient for tutoring_support_school:", round(np.mean(coefficient2), 4))
print("Average Coefficient for tutoring_support_private:", round(np.mean(coefficient3), 4))
print("Average Coefficient for region_urban:", round(np.mean(coefficient4), 4))
print("Average Coefficient for region_suburban:", round(np.mean(coefficient5), 4))
#print("Average Coefficient for region_rural:", round(np.mean(coefficient6), 4))
#print("Average GME for urban:", round(np.mean(GME_urban), 4))
#print("Average GME for suburban:", round(np.mean(GME_suburban), 4))
#print("Average GME for rural:", round(np.mean(GME_rural), 4))
#print("Average prediction for urban:", round(np.mean(meanprediction_urban), 4))
#print("Average prediction for suburban:", round(np.mean(meanprediction_suburban), 4))
#print("Average prediction for rural:", round(np.mean(meanprediction_rural), 4))

Ramsey RESET test 1 (F-test): <F test: F=1.48186788283807, p=0.2275261191286845, df_denom=1.59e+03, df_num=2>

C:\Users\Ibrou\AppData\Local\Temp\ipykernel_39192\3874247992.py:47: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`
  intercept.append(coefficients[0])
C:\Users\Ibrou\AppData\Local\Temp\ipykernel_39192\3874247992.py:48: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`
  coefficient1.append(coefficients[1])
C:\Users\Ibrou\AppData\Local\Temp\ipykernel_39192\3874247992.py:49: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`
  coefficient2.append(coefficients[2])
C:\Users\Ibrou\AppData\Local\Temp\ipykernel_39192\3874247992.py:50: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`
  coefficient3.append(coefficients[3])
C:\Users\Ibrou\AppData\Local\Temp\ipykernel_39192\3874247992.py:51: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`
  coefficient4.append(coefficients[4])
C:\Users\Ibrou\AppData\Local\Temp\ipykernel_39192\3874247992.py:52: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`
  coefficient5.append(coefficients[5])

Ramsey RESET test 2 (F-test): <F test: F=0.32087908966718337, p=0.7255578791515537, df_denom=1.59e+03, df_num=2>

C:\Users\Ibrou\AppData\Local\Temp\ipykernel_39192\3874247992.py:47: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`
  intercept.append(coefficients[0])
C:\Users\Ibrou\AppData\Local\Temp\ipykernel_39192\3874247992.py:48: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`
  coefficient1.append(coefficients[1])
C:\Users\Ibrou\AppData\Local\Temp\ipykernel_39192\3874247992.py:49: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`
  coefficient2.append(coefficients[2])
C:\Users\Ibrou\AppData\Local\Temp\ipykernel_39192\3874247992.py:50: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`
  coefficient3.append(coefficients[3])
C:\Users\Ibrou\AppData\Local\Temp\ipykernel_39192\3874247992.py:51: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`
  coefficient4.append(coefficients[4])
C:\Users\Ibrou\AppData\Local\Temp\ipykernel_39192\3874247992.py:52: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`
  coefficient5.append(coefficients[5])

C:\Users\Ibrou\AppData\Local\Temp\ipykernel_39192\3874247992.py:47: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`
  intercept.append(coefficients[0])
C:\Users\Ibrou\AppData\Local\Temp\ipykernel_39192\3874247992.py:48: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`
  coefficient1.append(coefficients[1])
C:\Users\Ibrou\AppData\Local\Temp\ipykernel_39192\3874247992.py:49: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`
  coefficient2.append(coefficients[2])
C:\Users\Ibrou\AppData\Local\Temp\ipykernel_39192\3874247992.py:50: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`
  coefficient3.append(coefficients[3])
C:\Users\Ibrou\AppData\Local\Temp\ipykernel_39192\3874247992.py:51: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`
  coefficient4.append(coefficients[4])
C:\Users\Ibrou\AppData\Local\Temp\ipykernel_39192\3874247992.py:52: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`
  coefficient5.append(coefficients[5])

Ramsey RESET test 3 (F-test): <F test: F=0.6544175872783571, p=0.5198844385835868, df_denom=1.59e+03, df_num=2>

Ramsey RESET test 4 (F-test): <F test: F=2.183742928154264, p=0.11295644693303862, df_denom=1.59e+03, df_num=2>

C:\Users\Ibrou\AppData\Local\Temp\ipykernel_39192\3874247992.py:47: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`
  intercept.append(coefficients[0])
C:\Users\Ibrou\AppData\Local\Temp\ipykernel_39192\3874247992.py:48: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`
  coefficient1.append(coefficients[1])
C:\Users\Ibrou\AppData\Local\Temp\ipykernel_39192\3874247992.py:49: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`
  coefficient2.append(coefficients[2])
C:\Users\Ibrou\AppData\Local\Temp\ipykernel_39192\3874247992.py:50: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`
  coefficient3.append(coefficients[3])
C:\Users\Ibrou\AppData\Local\Temp\ipykernel_39192\3874247992.py:51: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`
  coefficient4.append(coefficients[4])
C:\Users\Ibrou\AppData\Local\Temp\ipykernel_39192\3874247992.py:52: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`
  coefficient5.append(coefficients[5])

Ramsey RESET test 5 (F-test): <F test: F=0.5768955468899213, p=0.561756612186604, df_denom=1.59e+03, df_num=2>

C:\Users\Ibrou\AppData\Local\Temp\ipykernel_39192\3874247992.py:47: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`
  intercept.append(coefficients[0])
C:\Users\Ibrou\AppData\Local\Temp\ipykernel_39192\3874247992.py:48: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`
  coefficient1.append(coefficients[1])
C:\Users\Ibrou\AppData\Local\Temp\ipykernel_39192\3874247992.py:49: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`
  coefficient2.append(coefficients[2])
C:\Users\Ibrou\AppData\Local\Temp\ipykernel_39192\3874247992.py:50: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`
  coefficient3.append(coefficients[3])
C:\Users\Ibrou\AppData\Local\Temp\ipykernel_39192\3874247992.py:51: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`
  coefficient4.append(coefficients[4])
C:\Users\Ibrou\AppData\Local\Temp\ipykernel_39192\3874247992.py:52: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`
  coefficient5.append(coefficients[5])

df_model2 = df_model.drop(columns=["final_score"])

sns.heatmap(df_model2.corr(), annot=True, cmap='coolwarm')
plt.show()

	student_id	age	study_hours_per_week	attendance_rate	homework_completion	reading_score	math_score	science_score	parent_education_level	family_income	...	social_media_hours	gaming_hours	num_siblings	locker_number	bus_arrival_time	favorite_subject	final_exam_score	passed_course	college_admission	average_score
0	1	17	12.9	79.1	66.9	73.6	51.6	82.6	college	69815	...	3.1	1.7	2	A196	6	history	47.9	no	rejected	69.266667
1	2	18	16.6	97.2	78.2	70.6	56.9	80.7	graduate	76934	...	4.2	1.9	3	A289	8	math	58.9	no	rejected	69.400000
2	3	16	8.3	73.3	60.2	79.1	77.7	70.1	college	56996	...	1.4	2.3	1	A959	7	science	60.3	yes	rejected	75.633333
3	4	18	5.9	78.6	87.1	70.7	70.8	70.4	graduate	89833	...	5.2	2.7	1	A294	6	math	63.0	yes	rejected	70.633333
4	5	18	9.7	60.5	52.6	90.6	69.2	97.8	graduate	51160	...	2.8	2.9	0	A433	7	english	70.7	yes	rejected	85.866667

	student_id	age	study_hours_per_week	attendance_rate	homework_completion	reading_score	math_score	science_score	family_income	social_media_hours	gaming_hours	num_siblings	bus_arrival_time	final_exam_score	average_score
count	2000.000000	2000.000000	2000.000000	2000.000000	2000.00000	2000.000000	2000.000000	2000.000000	2000.000000	2000.000000	2000.000000	2000.0000	2000.000000	2000.000000	2000.000000
mean	1000.500000	15.991500	10.044950	79.815800	74.42150	69.900950	68.012300	71.870950	60424.172500	3.025050	2.000750	1.5080	7.015000	57.456300	69.928067
std	577.494589	1.430892	2.975495	11.495014	14.37666	10.514535	11.579182	10.881476	15225.326072	1.507197	1.201256	1.1084	0.818603	7.366265	6.336277
min	1.000000	14.000000	0.900000	60.000000	50.00000	31.600000	20.900000	34.900000	5472.000000	-1.700000	-1.700000	0.0000	6.000000	31.800000	50.200000
25%	500.750000	15.000000	8.100000	69.875000	62.00000	62.700000	60.200000	64.700000	50076.250000	2.000000	1.200000	1.0000	6.000000	52.400000	65.533333
50%	1000.500000	16.000000	10.000000	79.600000	74.20000	69.800000	68.250000	71.800000	60537.500000	3.000000	2.000000	1.0000	7.000000	57.400000	69.800000
75%	1500.250000	17.000000	12.000000	89.600000	86.80000	77.100000	75.700000	79.125000	70756.750000	4.100000	2.800000	2.0000	8.000000	62.525000	74.100000
max	2000.000000	18.000000	21.800000	100.000000	100.00000	105.300000	105.900000	109.200000	111434.000000	8.900000	6.600000	3.0000	8.000000	79.600000	91.233333

	student_id	age	study_hours_per_week	attendance_rate	homework_completion	reading_score	math_score	science_score	parent_education_level	family_income	...	social_media_hours	gaming_hours	num_siblings	locker_number	bus_arrival_time	favorite_subject	final_exam_score	passed_course	college_admission	average_score
count	2000.000000	2000.000000	2000.000000	2000.000000	2000.00000	2000.000000	2000.000000	2000.000000	2000	2000.000000	...	2000.000000	2000.000000	2000.0000	2000	2000.000000	2000	2000.000000	2000	2000	2000.000000
unique	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	4	NaN	...	NaN	NaN	NaN	801	NaN	5	NaN	2	2	NaN
top	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	high school	NaN	...	NaN	NaN	NaN	A871	NaN	english	NaN	no	rejected	NaN
freq	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	533	NaN	...	NaN	NaN	NaN	9	NaN	418	NaN	1270	1984	NaN
mean	1000.500000	15.991500	10.044950	79.815800	74.42150	69.900950	68.012300	71.870950	NaN	60424.172500	...	3.025050	2.000750	1.5080	NaN	7.015000	NaN	57.456300	NaN	NaN	69.928067
std	577.494589	1.430892	2.975495	11.495014	14.37666	10.514535	11.579182	10.881476	NaN	15225.326072	...	1.507197	1.201256	1.1084	NaN	0.818603	NaN	7.366265	NaN	NaN	6.336277
min	1.000000	14.000000	0.900000	60.000000	50.00000	31.600000	20.900000	34.900000	NaN	5472.000000	...	-1.700000	-1.700000	0.0000	NaN	6.000000	NaN	31.800000	NaN	NaN	50.200000
25%	500.750000	15.000000	8.100000	69.875000	62.00000	62.700000	60.200000	64.700000	NaN	50076.250000	...	2.000000	1.200000	1.0000	NaN	6.000000	NaN	52.400000	NaN	NaN	65.533333
50%	1000.500000	16.000000	10.000000	79.600000	74.20000	69.800000	68.250000	71.800000	NaN	60537.500000	...	3.000000	2.000000	1.0000	NaN	7.000000	NaN	57.400000	NaN	NaN	69.800000
75%	1500.250000	17.000000	12.000000	89.600000	86.80000	77.100000	75.700000	79.125000	NaN	70756.750000	...	4.100000	2.800000	2.0000	NaN	8.000000	NaN	62.525000	NaN	NaN	74.100000
max	2000.000000	18.000000	21.800000	100.000000	100.00000	105.300000	105.900000	109.200000	NaN	111434.000000	...	8.900000	6.600000	3.0000	NaN	8.000000	NaN	79.600000	NaN	NaN	91.233333

	age	study_hours_per_week	attendance_rate	homework_completion	reading_score	math_score	science_score	family_income	social_media_hours	gaming_hours	num_siblings	final_exam_score
0	17	12.9	79.1	66.9	73.6	51.6	82.6	69815	3.1	1.7	2	47.9
1	18	16.6	97.2	78.2	70.6	56.9	80.7	76934	4.2	1.9	3	58.9
2	16	8.3	73.3	60.2	79.1	77.7	70.1	56996	1.4	2.3	1	60.3
3	18	5.9	78.6	87.1	70.7	70.8	70.4	89833	5.2	2.7	1	63.0
4	18	9.7	60.5	52.6	90.6	69.2	97.8	51160	2.8	2.9	0	70.7
...	...	...	...	...	...	...	...	...	...	...	...	...
1995	14	12.1	68.2	86.5	60.8	65.3	69.8	31619	1.8	0.6	1	43.3
1996	18	10.9	88.4	52.6	72.5	72.0	77.9	57876	2.2	2.0	1	68.8
1997	14	7.0	60.8	94.2	45.6	61.2	61.5	86560	4.0	2.1	0	54.0
1998	18	7.5	76.8	93.1	68.2	69.7	62.7	42991	1.2	1.2	0	52.3
1999	16	13.7	91.0	72.2	67.9	74.9	72.7	61206	2.8	1.7	3	55.1

	age	study_hours_per_week	attendance_rate	homework_completion	reading_score	math_score	science_score	family_income	social_media_hours	gaming_hours	num_siblings	final_exam_score
0	17	12.9	79.1	66.9	73.6	51.6	82.6	69815	3.1	1.7	2	47.9
1	18	16.6	97.2	78.2	70.6	56.9	80.7	76934	4.2	1.9	3	58.9
2	16	8.3	73.3	60.2	79.1	77.7	70.1	56996	1.4	2.3	1	60.3
3	18	5.9	78.6	87.1	70.7	70.8	70.4	89833	5.2	2.7	1	63.0
4	18	9.7	60.5	52.6	90.6	69.2	97.8	51160	2.8	2.9	0	70.7
...	...	...	...	...	...	...	...	...	...	...	...	...
1995	14	12.1	68.2	86.5	60.8	65.3	69.8	31619	1.8	0.6	1	43.3
1996	18	10.9	88.4	52.6	72.5	72.0	77.9	57876	2.2	2.0	1	68.8
1997	14	7.0	60.8	94.2	45.6	61.2	61.5	86560	4.0	2.1	0	54.0
1998	18	7.5	76.8	93.1	68.2	69.7	62.7	42991	1.2	1.2	0	52.3
1999	16	13.7	91.0	72.2	67.9	74.9	72.7	61206	2.8	1.7	3	55.1

	final_score	tutoring_support	region	math_score	reading_score	science_score
0	69.266667	school	urban	51.6	73.6	82.6
1	69.400000	none	suburban	56.9	70.6	80.7
2	75.633333	school	urban	77.7	79.1	70.1
3	70.633333	none	rural	70.8	70.7	70.4
4	85.866667	private	suburban	69.2	90.6	97.8

	math_score	reading_score	science_score	tutoring_support_private	tutoring_support_school	region_suburban	region_urban	final_score	average_score
0	-1.417752	0.351891	0.986239	0.0	1.0	0.0	1.0	69.266667	-0.026540
1	-0.959919	0.066501	0.811586	0.0	0.0	1.0	0.0	69.400000	-0.027277
2	0.836857	0.875108	-0.162790	0.0	1.0	0.0	1.0	75.633333	0.516392
3	0.240811	0.076014	-0.135213	0.0	0.0	0.0	0.0	70.633333	0.060537
4	0.102598	1.969105	2.383457	1.0	0.0	1.0	0.0	85.866667	1.485053